A246016 a(n) = (-1)^A055941(n).

1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1

Offset

0

Comments

This sequence and A246017 are the subject of the Lafrance et al. (2014) paper.

Links

Table of n, a(n) for n=0..85.

Philip Lafrance, Narad Rampersad, Randy Yee, Some properties of a Rudin-Shapiro-like sequence, arXiv:1408.2277 [math.CO], 2014.

Mathematica

b[n_] := b[n] = If[n == 0, 0, If[EvenQ[n], b[n/2] + DigitCount[n/2, 2, 1], b[(n-1)/2] + 1]];
a55941[n_] := b[n] - DigitCount[n, 2, 1];
a[n_] := (-1)^a55941[n];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 23 2018 *)

Prog

(PARI) a055941(n) = {my(b=binary(n)); nb = 0; for (i=1, #b-1, if (b[i], nb += sum(j=i+1, #b, !b[j])); ); nb; }
a(n) = (-1)^a055941(n);
(Python)
def A246016(n):
    a, b = 0, 0
    for i, j in enumerate(bin(n)[:1:-1]):
        if int(j):
            a ^= (i&1)^b
            b ^= 1
    return -1 if a else 1 # Chai Wah Wu, Jul 26 2023

Crossrefs

Cf. A055941, A161511, A246017 (partial sums).

Sequence in context: A292117 A098417 A143622 * A306638 A076479 A155040

Adjacent sequences: A246013 A246014 A246015 * A246017 A246018 A246019

Keyword

sign

Author

Michel Marcus and N. J. A. Sloane, Aug 13 2014

Status

approved